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A man gave 50% of his savings of Rs.84,100 to his wife and divided the remaining sum among his two sons A and B of 15 and 13 years of age respectively. He divided it in such a way that each of his sons, when they attain the age of 18 years, would receive the same amount at 5% compound interest per annum. The share of B was?
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A man gave 50% of his savings of Rs.84,100 to his wife and divided the...
Total savings
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Amount
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Amount of
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A man gave 50% of his savings of Rs.84,100 to his wife and divided the...
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A man gave 50% of his savings of Rs.84,100 to his wife and divided the...
Given:
- Total savings of a man = Rs. 84,100
- He gave 50% of his savings to his wife
- The remaining sum is divided among his two sons A and B
- The ages of sons A and B are 15 years and 13 years respectively
- Each son will receive the same amount at 5% compound interest per annum when they attain the age of 18 years
To Find:
The share of son B
Solution:
Step 1: Calculate the amount given to his wife
- 50% of Rs. 84,100 = (50/100) * 84,100 = Rs. 42,050
Step 2: Calculate the remaining sum
- Remaining sum = Total savings - Amount given to wife
- Remaining sum = Rs. 84,100 - Rs. 42,050 = Rs. 42,050
Step 3: Calculate the amount each son will receive at the age of 18 years
- Since the amount is divided equally among the sons, let's assume the amount as 'x'
- The compounding interest formula is given by: A = P * (1 + r/n)^(nt)
where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the time in years
- In this case, the principal amount is 'x', the interest rate is 5%, the interest is compounded annually, and the time is 3 years (from 15 years to 18 years)
- For son A: A = x * (1 + 0.05/1)^(1*3) = x * (1.05)^3
- For son B: A = x * (1 + 0.05/1)^(1*5) = x * (1.05)^5
Step 4: Equate the amounts received by sons A and B at the age of 18 years
- x * (1.05)^3 = x * (1.05)^5
- (1.05)^3 = (1.05)^5
- Canceling out 'x' from both sides, we get:
- (1.05)^3 = (1.05)^5
- 1.157625 = 1.27628125
Step 5: Solve for x
- We can take the cube root of both sides to solve for x:
- (1.05)^3 = (1.05)^5
- 1.05 = 1.05^(5/3)
- 1.05 = 1.091393684
- x = Rs. 38,594.48
Step 6: Calculate the share of son B
- Since the amount is divided equally, the share of son B is:
- Share of son B = x
- Share of son B = Rs. 38,594.48
Answer:
The share of son B is Rs. 38,594.48.
- Total savings of a man = Rs. 84,100
- He gave 50% of his savings to his wife
- The remaining sum is divided among his two sons A and B
- The ages of sons A and B are 15 years and 13 years respectively
- Each son will receive the same amount at 5% compound interest per annum when they attain the age of 18 years
To Find:
The share of son B
Solution:
Step 1: Calculate the amount given to his wife
- 50% of Rs. 84,100 = (50/100) * 84,100 = Rs. 42,050
Step 2: Calculate the remaining sum
- Remaining sum = Total savings - Amount given to wife
- Remaining sum = Rs. 84,100 - Rs. 42,050 = Rs. 42,050
Step 3: Calculate the amount each son will receive at the age of 18 years
- Since the amount is divided equally among the sons, let's assume the amount as 'x'
- The compounding interest formula is given by: A = P * (1 + r/n)^(nt)
where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the time in years
- In this case, the principal amount is 'x', the interest rate is 5%, the interest is compounded annually, and the time is 3 years (from 15 years to 18 years)
- For son A: A = x * (1 + 0.05/1)^(1*3) = x * (1.05)^3
- For son B: A = x * (1 + 0.05/1)^(1*5) = x * (1.05)^5
Step 4: Equate the amounts received by sons A and B at the age of 18 years
- x * (1.05)^3 = x * (1.05)^5
- (1.05)^3 = (1.05)^5
- Canceling out 'x' from both sides, we get:
- (1.05)^3 = (1.05)^5
- 1.157625 = 1.27628125
Step 5: Solve for x
- We can take the cube root of both sides to solve for x:
- (1.05)^3 = (1.05)^5
- 1.05 = 1.05^(5/3)
- 1.05 = 1.091393684
- x = Rs. 38,594.48
Step 6: Calculate the share of son B
- Since the amount is divided equally, the share of son B is:
- Share of son B = x
- Share of son B = Rs. 38,594.48
Answer:
The share of son B is Rs. 38,594.48.
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A man gave 50% of his savings of Rs.84,100 to his wife and divided the remaining sum among his two sons A and B of 15 and 13 years of age respectively. He divided it in such a way that each of his sons, when they attain the age of 18 years, would receive the same amount at 5% compound interest per annum. The share of B was?
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A man gave 50% of his savings of Rs.84,100 to his wife and divided the remaining sum among his two sons A and B of 15 and 13 years of age respectively. He divided it in such a way that each of his sons, when they attain the age of 18 years, would receive the same amount at 5% compound interest per annum. The share of B was? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A man gave 50% of his savings of Rs.84,100 to his wife and divided the remaining sum among his two sons A and B of 15 and 13 years of age respectively. He divided it in such a way that each of his sons, when they attain the age of 18 years, would receive the same amount at 5% compound interest per annum. The share of B was? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man gave 50% of his savings of Rs.84,100 to his wife and divided the remaining sum among his two sons A and B of 15 and 13 years of age respectively. He divided it in such a way that each of his sons, when they attain the age of 18 years, would receive the same amount at 5% compound interest per annum. The share of B was?.
A man gave 50% of his savings of Rs.84,100 to his wife and divided the remaining sum among his two sons A and B of 15 and 13 years of age respectively. He divided it in such a way that each of his sons, when they attain the age of 18 years, would receive the same amount at 5% compound interest per annum. The share of B was? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A man gave 50% of his savings of Rs.84,100 to his wife and divided the remaining sum among his two sons A and B of 15 and 13 years of age respectively. He divided it in such a way that each of his sons, when they attain the age of 18 years, would receive the same amount at 5% compound interest per annum. The share of B was? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man gave 50% of his savings of Rs.84,100 to his wife and divided the remaining sum among his two sons A and B of 15 and 13 years of age respectively. He divided it in such a way that each of his sons, when they attain the age of 18 years, would receive the same amount at 5% compound interest per annum. The share of B was?.
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A man gave 50% of his savings of Rs.84,100 to his wife and divided the remaining sum among his two sons A and B of 15 and 13 years of age respectively. He divided it in such a way that each of his sons, when they attain the age of 18 years, would receive the same amount at 5% compound interest per annum. The share of B was?, a detailed solution for A man gave 50% of his savings of Rs.84,100 to his wife and divided the remaining sum among his two sons A and B of 15 and 13 years of age respectively. He divided it in such a way that each of his sons, when they attain the age of 18 years, would receive the same amount at 5% compound interest per annum. The share of B was? has been provided alongside types of A man gave 50% of his savings of Rs.84,100 to his wife and divided the remaining sum among his two sons A and B of 15 and 13 years of age respectively. He divided it in such a way that each of his sons, when they attain the age of 18 years, would receive the same amount at 5% compound interest per annum. The share of B was? theory, EduRev gives you an
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